TY - JOUR
T1 - On matrix characterizations for P-property of the linear transformation in second-order cone linear complementarity problems
AU - Miao, Xin He
AU - Chen, Jein Shan
N1 - Publisher Copyright:
© 2020 Elsevier Inc.
PY - 2021/3/15
Y1 - 2021/3/15
N2 - The P-property of the linear transformation in second-order cone linear complementarity problems (SOCLCP) plays an important role in checking the globally uniquely solvable (GUS) property due to the work of Gowda et al. However, it is not easy to verify the P-property of the linear transformation, in general. In this paper, we provide matrix characterizations for checking the P-property, which is a new approach different from those in the literature. This is a do-able manipulation, which helps verifications of the P-property and globally uniquely solvable (GUS) property in second-order cone linear complementarity problems. Moreover, using an equivalence relation to the second-order cone linear complementarity problem, we study some sufficient and necessary conditions for the unique solution of the absolute value equations associated with second-order cone (SOCAVE).
AB - The P-property of the linear transformation in second-order cone linear complementarity problems (SOCLCP) plays an important role in checking the globally uniquely solvable (GUS) property due to the work of Gowda et al. However, it is not easy to verify the P-property of the linear transformation, in general. In this paper, we provide matrix characterizations for checking the P-property, which is a new approach different from those in the literature. This is a do-able manipulation, which helps verifications of the P-property and globally uniquely solvable (GUS) property in second-order cone linear complementarity problems. Moreover, using an equivalence relation to the second-order cone linear complementarity problem, we study some sufficient and necessary conditions for the unique solution of the absolute value equations associated with second-order cone (SOCAVE).
KW - Absolute value equations
KW - Globally uniquely solvable property
KW - P-property
KW - Second-order cone linear complementarity problem
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U2 - 10.1016/j.laa.2020.11.010
DO - 10.1016/j.laa.2020.11.010
M3 - Article
AN - SCOPUS:85096574737
SN - 0024-3795
VL - 613
SP - 271
EP - 294
JO - Linear Algebra and Its Applications
JF - Linear Algebra and Its Applications
ER -